Summary of Work: This project is intended to increase our understanding of the use and application of mathematical and statistical models in toxicology and biochemistry and to implement new mathematical models to aid in explaining current research findings. The research effort explores a diverse range of biological areas, including carcinogenesis, pharmacology, developmental biology, neurology, immunology and endocrinology. Major accomplishments include (1) the derivation of methods for the analysis of carcinogenicity data including data on papillomas, carcinomas and maintaining tissue size (2) new stochastic models of carcinogenesis which account for intercellular communication and epigenetic progression (3) methods were developed for linking PBPK models, premalignant lesion data, cell labelling data and tumor incidence data (4) models for mortality/morbidity in urban areas are being validated in a Japanese population (5) exposure assessment models have been developed (6) built and experimentally validated a mathematical model describing the specific phases of the cell cycle (7) developed methods for assessing shapes of dose-response curves and for using QSAR to aid in the estimation of shape, (8) used QSAR techniques to develop PBPK models for the entire class of PCB's and (9) continued to aid in the scientific improvement of risk assessment methods through the application of sound science to key environmental issues such as exposure to TCDD, aflatoxins and endocrine disruptors.